A wire of cross sectional area A, modulus of elasticity 2 × 10^11 Nm^-2 and length 2 m is stretched between two vertical rigid supports. When a mass…

A wire of cross sectional area A , modulus of elasticity $\displaystyle 2 \times 10^{11} \mathrm{Nm}^{-2}$ and length $\displaystyle 2$ m is stretched between two vertical rigid supports. When a mass of $\displaystyle 2$ kg is suspended at the middle it sags lower from its original position making angle $\displaystyle \theta=\frac{1}{100}$ radian on the points of support. The value of A is $\displaystyle \_\_\_\_$ $\displaystyle \times 10^{-4} \mathrm{~m}^2$ (consider $\displaystyle x \ll \mathrm{~L}$ ). (given : $\displaystyle g=10 \mathrm{~m} / \mathrm{s}^2$ )